Introduction to Health Physics: Fourth Edition - Ruang Baca FMIPA UB

Evaluation of Radiation Safety Measures 691
airflow is increased, the velocity of the air flowing through the annular space between
the ball and the inside surface of the rotameter increases, thereby increasing the
viscous force. This increased viscous force drags the ball upward, where the larger
annular space leads to a decreased air velocity. At the height where the velocity of the
increased volume of air through the annular space leads to a viscous force exactly
equal to the gravitational force acting on the ball, the ball will come to rest. The new
equilibrium position tells us what the new volumetric flow rate is.
The viscosity of the air depends on its density, which in turn depends on the
temperature and pressure. If the rotameter is used at a temperature or pressure
that differs significantly from the conditions under which it was calibrated, then
the observed reading must be corrected to account for the different air density. The
actual flow rate, Qa, is related to the calibration reading of the rotameter, Q0, by
ρ0
Qa = Q0 = Q0
ρa
p0/T0
pa/Ta
= Q0
p0
pa
× Ta
, (13.20)
T0
where the calibration and actual temperatures T0 and Ta are in degrees absolute.
W EXAMPLE 13.6
The rotameter on a pump was calibrated to read 2.0 L/min at an altitude of
575 ft (175 m), where the pressure was 29.31 in. Hg (745 mm Hg) and the temperature
was 75 ◦ F (24 ◦ C). The pump was used in a uranium mine at an altitude of
7000 ft (2134 m), where the atmospheric pressure was 23.10 in. Hg (587 mm Hg)
and the temperature 50 ◦ F (10 ◦ C).
(a) What was the actual flow rate if the rotameter reading was 2.0 L/min?
(b) What should the rotameter reading be for an actual flow rate of 2.0 L/min?
Solution
(a) If we substitute the respective values into Eq. (13.20), we find the actual flow
rate to be
29.31 460 + 50 L
Qa = 2.0 × × = 2.2
23.10 460 + 75 min .
(b) Substituting into Eq. (13.20) and then solving for Q0, we have
2 L
min = Q0
29.31 460 + 50
× ×
23.10 460 + 75
Q0 = 1.8 L/min.